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A004014 Norms of vectors in the b.c.c. lattice.
(Formerly M2347)
4
0, 3, 4, 8, 11, 12, 16, 19, 20, 24, 27, 32, 35, 36, 40, 43, 44, 48, 51, 52, 56, 59, 64, 67, 68, 72, 75, 76, 80, 83, 84, 88, 91, 96, 99, 100, 104, 107, 108, 115, 116, 120, 123, 128, 131, 132, 136, 139, 140, 144, 147, 148, 152, 155, 160, 163, 164, 168 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Integers such that A004013(n) is nonzero. - Michael Somos, Jul 28 2014
A subsequence of A047458. The complement seems to be 4*A004215. - Andrey Zabolotskiy, Nov 11 2021
From Mohammed Yaseen, Nov 06 2022: (Start)
These are numbers of the form x^2+y^2+z^2 where x, y and z are either all even (including zero) or all odd.
The selection rule for the planes with Miller indices (hkl) to undergo X-ray diffraction in an f.c.c. lattice is h^2+k^2+l^2 = N where N is a term of this sequence. See A000378 for simple cubic lattice. (End)
REFERENCES
J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 116. (Chapter 4 section 6.7)
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
G. Nebe and N. J. A. Sloane, Home page for this lattice
MAPLE
f:= JacobiTheta2(0, z^4)^3+JacobiTheta3(0, z^4)^3:
S:= series(f, z, 1001):
select(t -> coeff(S, z, t) <> 0, [$0..1000]); # Robert Israel, Oct 18 2015
MATHEMATICA
f = EllipticTheta[2, 0, z^4]^3 + EllipticTheta[3, 0, z^4]^3; S = f + O[z]^200; Flatten[Position[CoefficientList[S, z], _?Positive] - 1] (* Jean-François Alcover, Oct 23 2016, after Robert Israel *)
CROSSREFS
Union of A034045 and A017101. - Mohammed Yaseen, Nov 06 2022
Sequence in context: A222269 A310011 A047458 * A243177 A113294 A169691
KEYWORD
nonn,nice,easy
AUTHOR
EXTENSIONS
More terms from Sean A. Irvine, Oct 17 2015
STATUS
approved

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Last modified April 16 20:04 EDT 2024. Contains 371754 sequences. (Running on oeis4.)